Applied Systems Theory: Mathematical and Numerical Simulation of Strength of Thick-wall Pipe by Using Static Elastic Problems

Abstract

In Systems Theory, the Mathematical and numerical simulation of strength of thick-wall pipe by using static elastic problems is an important problem and has attracted the attention of many researches, academicians and practitioners. the The present work studies the change in the strength of a quite long isotropic thick-wall pipe (circular cylinder) for the varying pipe diameter, wall thickness and material. The pipe is in the plane deformed state, i.e. plane deformation is considered. Based on the problems of statics of the theory of elasticity, a mathematical model to calculate the strength of the thick-wall pipe was developed and the problems of statics of the theory of elasticity were set and solved analytically in the polar coordinate system. The analytical solution was obtained by the method of separation of variables, which is presented by two harmonious functions. The dependence of the pipe strength on the thickness and material of the pipe wall, when (a) normal stress is applied to the internal boundary (internal pressure) and external boundary is free from stresses and (b) normal stress is applied to the external boundary (external pressure) and the internal boundary is free from stresses, is studied. In particular, the minimum thicknesses of the walls of homogeneous isotropic circular cylinders of different materials and diameters with a plane deformed mode when the pressures in the cylinders do not exceed the admissible values were identified. Some numerical results are presented as tables, graphs and relevant consideration.